The register
The register lists The Thin White Duke in London as a licensed sponsor on Skilled Worker, an entry that goes back to at least 2026. Its rating on the register is Worker (A rating).
Companies House lists it as The Thin White Duke Limited, number 13350197, incorporated 2021: 5 years of filings behind the name. The registered office is at Flat K, 59 Warwick Square, London, SW1V 2AL, SW1V 2AL. Its filed activity puts it in manufacturing. It has traded under other names before, including Lyon's Pride Limited.
Holding a licence is the expensive, slow part done. For The Thin White Duke the question each time is only whether the role and the pay fit the current rules, and that is checked per vacancy.